TY - JOUR

T1 - Mocking the u-plane integral

AU - Korpas, Georgios

AU - Manschot, Jan

AU - Moore, Gregory W.

AU - Nidaiev, Iurii

N1 - Funding Information:
We thank Johannes Aspman, Aliakbar Daemi, Elias Furrer, Lothar Göttsche, Jeff Harvey, John Morgan, Tom Mrowka and Hiraku Nakajima for discussions. GK would like to thank the Institute Of Pure and Applied Mathematics of UCLA and the Physics Department of the National and Kapodistrian University of Athens for hospitality. JM would like to thank the NHETC, Rutgers University for hospitality. JM is supported by the Laureate Award 15175 “Modularity in Quantum Field Theory and Gravity” of the Irish Research Council. GM and IN are supported by the US Department of Energy under grant DE-SC0010008.
Funding Information:
We thank Johannes Aspman, Aliakbar Daemi, Elias Furrer, Lothar G?ttsche, Jeff Harvey, John Morgan, Tom Mrowka and Hiraku Nakajima for discussions. GK would like to thank the Institute Of Pure and Applied Mathematics of UCLA and the Physics Department of the National and Kapodistrian University of Athens for hospitality. JM would like to thank the NHETC, Rutgers University for hospitality. JM is supported by the Laureate Award 15175 ?Modularity in Quantum Field Theory and Gravity? of the Irish Research Council. GM and IN are supported by the US Department of Energy under grant DE-SC0010008.
Publisher Copyright:
© 2021, The Author(s).

PY - 2021/9

Y1 - 2021/9

N2 - The u-plane integral is the contribution of the Coulomb branch to correlation functions of N= 2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group SU (2) , for an arbitrary four-manifold with (b1,b2+)=(0,1). The u-plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u-plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

AB - The u-plane integral is the contribution of the Coulomb branch to correlation functions of N= 2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group SU (2) , for an arbitrary four-manifold with (b1,b2+)=(0,1). The u-plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u-plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

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U2 - 10.1007/s40687-021-00280-5

DO - 10.1007/s40687-021-00280-5

M3 - Article

AN - SCOPUS:85108848701

SN - 2522-0144

VL - 8

JO - Research in Mathematical Sciences

JF - Research in Mathematical Sciences

IS - 3

M1 - 43

ER -